The super multibracket of order \(n\)  is defined as [1]}:

\(\Big [A_1,A_2,\cdots ,A_n\Big ]:=\epsilon ^{i_1i_2\cdots i_n}_{12\cdots n}\big (-1\big )^{\sum _{k=1}^{n-1}|A_k|(\sum _{l=k+1,i_l< i_k}^{n}|A_{i_l}|)}\,A_{i_1}\,A_{i_2}\cdots A_{i_n},\) 
